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Denominate Numbers - Volume Measure.

343. An ordinary brick is 2 in. by 4 in. by 8 in. and weighs about 4 pounds.

PROBLEMS.

1. How many bricks are equivalent to 1 cubic foot ?

NOTE.-When bricks are laid in mortar in the usual way, about 22 bricks are required to make a cubic foot of wall.

2. Estimate the number of bricks necessary for a cellar wall 12 inches thick, the inside dimensions of the cellar being 15 feet by 18 feet, and 7 feet deep, no allowance being made for openings in the wall ?

3. What are the outside dimensions of the wall of the cellar described in problem 2?

4.. What length of wall 7 feet high and 12 inches thick is equivalent, so far as the number of bricks required is concerned, to the cellar wall described in problem 2?

5. If of the depth of the cellar described above is to be below the surface, how many cubic yards of earth must be excavated ?

6. Estimate the number of bricks necessary for a wall 100 yards long, 11 feet high, and 1 foot thick.

7. If a brick is exactly 2 in. by 4 in. by 8 in. and weighs exactly 44 lbs. what is its specific gravity ?*

8. Find the approximate weight (in tons) of a pile of bricks as long as your school-room, 2 feet wide, and 4 feet high.

9. Find the approximate weight of a chimney, outside dimensions, 16 in. by 16 in., and 20 ft. high, the flue being 8 in. by 8 in.

* Compare the weight of 27 such bricks with the weight of a cubic foot of water.

Denominate Numbers-Lumber.

344. A foot of lumber is a board 1 foot square and 1 inch thick or its equivalent.

Note 1.-An exception to the foregoing is made in the measurement of boards less than 1 inch in thickness. A square foot of such boards is regarded as a foot of lumber whatever the thickness.

Observe that a piece of board 1 inch wide, 1 inch thick, and 12 feet long, is I foot of lumber.

EXERCISE.

Tell the number of feet of lumber in each of the following boards, the thickness in each case being 1 inch (or less):

1 in. wide and 12 ft. long. 2 in. wide and 12 ft. long. 3 in. wide and 12 ft. long. 4 in. wide and 12 ft. long. 7 in. wide and 12 ft. long. 13 in. wide and 12 ft. long. 9 in. wide and 12 ft. long. 12 in. wide and 12 ft. long. (a) How many feet (of lumber) in the eight boards?

PROBLEMS.

1. How much lumber in 6, 12-ft., 1-in. boards whose widths are 11 in., 13 in., 9 in., 10 in., 12 in., and 14 in. ?

2. How much lumber in 5, 12-ft. 4-in. boards whose widths are 10 in., 12 in., 12 in., 11 in., and 14 in. ?

3. How much lumber in 7, 12-ft. 4-in. boards whose widths are 9 in., 8 in., 5 in., 7 in., 8 in., 6 in., and 9 in. ?

4. How much lumber in 8, 12-ft., 1-in. boards each of which is 12 inches wide ?

5. How much lumber in 54, 12-ft. 1-in. boards each of which is 6 inches wide ?

(b) Find the sum of the five results.

Denominate Numbers-Lumber.

PROBLEMS. NOTE 2.-A 14-foot board contains & more lumber than a 12-ft. board of the same width and thickness. Hence to find the number of feet of lumber in 14-foot boards, find the number of feet in as many 12-foot boards * and add to the result & of itself.

1. How much lumber in 6, 14-ft., 1-in. boards whose widths are 11 in., 12 in., 12 in., 15 in., 10 in., and 13 in. ?

2. How much lumber in a pile of 14-ft. boards whose united width is 8 feet 7 inches ?

3. How much lumber in 56, 14-ft. boards each of which is 6 inches wide? +

4. How much lumber in 24, 14-ft. boards each of which is 12 inches wide ? I

(a) Find the sum of the four results.

PROBLEMS. NOTE 3.– A 16-foot board contains { more lumber than a 12-foot board of the same width and thickness. Make a rule for finding the number of feet of lumber in 16-foot boards.

1. How much lumber in 6, 16-ft. 1-in. boards whose widths are 12 in., 10 in , 14 in., 13 in., 12 in., and 10 in. ?

2. How much lumber in a pile of 16-foot boards whose united width is 9 feet 8 inches ?

3. How much lumber in 48, 16-ft. boards each of which is 6 inches wide?

4. How much lumber in 34, 16-ft. boards each of which is 12 inches wide ?

(b) Find the sum of the four results.

* Take the nearest integral number of feet,
+ How much lumber in 1 14-foot board 6 inches wide ?
How much lumber in 1 14-foot board 12 inches wide ?

Denominate Numbers—Lumber.

PROBLEMS.

NOTE 4-A 14-inch board contains more lumber than a 1-inch board of the same width and length. A 1;-inch board contains į more íumber than a 1-inch board of the same width and length.

1. How much lumber in 4, 12-foot, 14-in. boards whose widths are 12 in., 13 in., 14 in., and 13 in. ?

2. How much lumber in 4, 16-foot, 11-in. boards whose widths are 13 in., 16 in., 12 in., and 13 in. ?

3. How much lumber in 4, 18-foot, 11-in. boards, each of which is 12 inches wide ?

4. How much lumber in 4, 16-ft., 14-in. boards, each of which is 6 inches wide ?

(a) Find the sum of the four results.

PROBLEMS. NOTE 5.-A.“ 2 by 4, 12” is a piece of lumber 2 in. thick, 4 in. wide, and 12 feet long.

Find the number of feet of lumber in each of the following items :

1. 16 pieces 2 x 4, 12.
2. 18 pieces 4 x 4, 12.
3. 25 pieces 2 x 8, 12.
4. 30 pieces 2 ~ 6, 12.
5. 20 pieces 4 ~ 6, 12.

6. 32 pieces 6 ~ 6, 12.
(b) Find the sum of the six results.

Observe that in a 12-foot piece of lumber there are as many feet as there are square inches in the cross-section. A piece of lumber 1 in. by 1 in. and 12 feet long is 1 foot of lumber; a piece 2 in. by 2 in. is 4 feet of lumber; a piece 2 in. by 3 in. is 6 feet of lumber, etc.

Denominate Numbers-Lumber.

PROBLEMS.

Note 6.-In the measurement of timbers of all sizes it is customary to consider each piece as containing the integral number of feet nearest to the actual content. Thus, a piece of 2 X 4, 14, actually contains 9j feet, but in all lumber yards it is counted as 9 feet. A piece of 2 X 4, 16, actually contains 103 feet, but it is counted as 11 feet.

Find the number of feet of lumber in each of the following items :

1. 16 pieces 2 x 4, 14.*
2. 24 pieces 4 x 4, 14.
3. 32 pieces 2 x 8, 14.
4. 17 pieces 4 x 6, 14.
5. 15 pieces 8 x 8, 16.
6. 12 pieces 4 x 10, 16.
7. 14 pieces 8 x 12, 16.

8. 6 pieces 12 x 12, 24.
(a) Find the sum of the eight results.

PROBLEMS.

Note 7.-"Lumber at $15 per M,” means that the lumber is sold at the rate of $15 per 1000 feet.

Find the cost :

1. 26, 16-foot, 6-in. fence boards @ $15 per M.
2. 34, 14-foot, 12-in. stock boards“ $18 per M.
3. 20 pieces 2 x 4, 16,

$16 per M.
4. 14 pieces 4x 6, 18,

$16
per

M.
5. 25 pieces 4 ~ 6, 16,

$15
per

M.
6. 18 pieces 4 x 4, 14,

$15
per

M. (b) Find the sum of the six results. * Find the number of feet in 1 piece of 2 X 4, 14 (nearest whole number of feet) and multiply by 16.

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